Abstract
Given a commutative noetherian non-positive DG-ring with bounded cohomology which has a dualizing DG-mo dule, we study its regular, Gorenstein and Cohen-Macaulay loci. We give a sufficient condition for the regular locus to be open, and show that the Gorenstein locus is always open.
However, both of these loci are often empty: we show that no matter how nice H-0(A) is, there are examples where the Gorenstein locus of A is empty. We then show that the Cohen-Macaulay locus of a commutative noetherian DG-ring with bounded cohomology which has a dualizing DG-mo dule always contains a dense open set.
Our results imply that under mild hypothesis, eventually coconnective locally noetherian derived schemes are generically Cohen-Macaulay, but even in very nice cases, they need not be generically Gorenstein. (c) 2021 Elsevier B.V. All rights reserved.